Washing machine in the bathroom

Merry Christmas! I am in the process of buying a portable washer (or a top loader) for the bathroom since there is not much room. But the only water supply available seems to be the single handle faucet (Photo attached). Now I was told the washer could actually damage the facet and I would need to find a special washer with some sort of "slow" valve. I am here and would like your opinion on this. Is that true that the washing mating could damage the faucet and if yes is there anything I could do or do? Thanks!